linear algebra and C++ (1998 – Present) • The Eigen C++ Template Library for Linear Algebra • Linear Algebra Interface in C++26 • Basics • Using with Eigen Outline Daniel Hanson CppCon 2024 2• This This presentation is on solving problems using • The Eigen linear algebra library • stdBLAS in C++26 • Not affiliated with Eigen but have used it in financial programming and teaching • Goal is to share Libraries Daniel Hanson CppCon 2024 6• “Next Generation” linear algebra libraries (not exhaustive): • Eigen (2006) • Armadillo (2009) • Blaze (2012) • Expression template-based libraries • Include the usual

Concurrency) • Obtain statistical properties of the tumors (Parallel STL algorithms) • Eigen (Array Class) • Eigen is a C++ template library for linear algebra: matrices, vectors, numerical solvers, Cell that grows abnormally Cell dynamics: 𝑢23 𝜆2 𝑢01 𝑢12 #include <Eigen/Dense> class TumorGenerator { Eigen::ArrayXd initial_population; double tmax; double dt; //... The Array class template: Array typedef Eigen::ArrayEigen::Dynamic,1> Eigen::ArrayXd; tmax = 0 20 40 60 80 dt = 20 6 0 0 0 cppreference.comTransition

【fast_forward kinematics_ Library code_generation) (fast_forward _kinematics_ Library LBFGSpp) (Eigen3 ) {fast_forward_kinematics library (fast_forward_kinematics_ Library (fast_forward_kinematics_ kinematics_ Library (fast_forward_kinematics Library CMAKE SOURCE_DIR]/: LBFGSppIncLudeDir}) Eigen3::Eigen) Eigen3::Eigen) rootQ7fda3b6daf26:~/fast_robot_kinematics# cmake -BbutLd -S. -- The C compitLer identification t ind， vatue， Eigenz :Vector< ，Ti:get_num_joints()> &vatues， Eigen: :Vector< ，Ti:get_num_joints()> &vatues_non_const， Eigen::VectorX &q_guess) Ti:get num_ joints() }; { obj,set joint(ind，vatue)

ew()} {} } // namespace robot_joint cpp 12class Joint { public: Eigen::Isometry3d calculate_transform(const Eigen::VectorXd& variables); }; impl Joint { pub fn calculate_transform(&self int*, const double*, unsigned int); } cpp 16namespace robot_joint { Eigen::Isometry3d Joint::calculate_transform( const Eigen::VectorXd& variables ) { const auto rust_isometry = robot_joint_calculate_transform( size()); Eigen::Isometry3d transform; transform.matrix() = Eigen::Map<Eigen::Matrix4d>(rust_isometry.data); return transform; } } // namespace robot_joint cpp 17class Joint { public: Eigen::Isometry3d

FILE_SET) 27 add_library(Eigen INTERFACE) target_sources(Eigen INTERFACE FILE_SET HEADERS BASE_DIRS src FILES src/eigen.h src/vector.h src/matrix.h ) install(TARGETS Eigen EXPORT eigenExport FILE_SET HEADERS DESTINATION include/Eigen) install(EXPORT eigenExport NAMESPACE Upstream:: DESTINATION lib/cmake/Eigen ) add_executable(exe1 exe1.cpp) target_link_libraries(exe1 Eigen)Running Install 28 # running st/include/Eigen/eigen.h -- Installing: C:/Users/hoffman/Work/cxxmodules/file_set/b/inst/include/Eigen/vector.h -- Installing: C:/Users/hoffman/Work/cxxmodules/file_set/b/inst/include/Eigen/matrix.h --

Handle Segment 1 Segment 2 Segment 3 CameraOne way of solving this problem… using Transform = Eigen::Isometry3d; using Joint = std::variant; class Fixed { Transform this problem… class Revolute { Transform fixed_; Eigen::Vector3d axis_; … Transform pose(double position) const { return fixed_ * Eigen::AngleAxisd(position, axis_); } };One way of solving this problem… class Prismatic { … Transform pose(double position) const { return fixed_ * Eigen::Translation3d(position * axis_); } };Requisite godbolt.org demo • https://godbolt.org/z/5jM9sa3vYReducing

Usage Exampleatomosspace.com | 31 inline constexpr Eigen::Matrix runge_kutta4(std::function<Eigen::Matrix(double, Eigen::Matrix)> fun, double time, Eigen::Matrix y0, double timestep) { auto k1 = fun(time, y0); auto k2 = fun(time + timestep * 0.5, y0 return (y0 + (k1 + 2 * k2 + 2 * k3 + k4) * timestep / 6); } Eigen::Matrix stateOut = common::math::runge_kutta4Eigen::Matrix>(derivFun, currTime, stateIn, dt); Usage

imported LinearAlgebra standard library into scope as LA. import LinearAlgebra: eigen as eig, cholesky as chol brings the eigen and cholesky meth- ods from LinearAlgebra into scope as eig and chol respectively individual identifiers are brought into scope. For example, using LinearAlgebra: eigen as eig or using LinearAlgebra: eigen as eig, cholesky as chol works, but using LinearAlgebra as LA is invalid syntax method for matrix-scalar operations is availableCHAPTER 77. LINEAR ALGEBRA 1231 Matrix type LAPACK eigen eigvals eigvecs svd svdvals Symmetric SY ARI Hermitian HE ARI UpperTriangular TR A A A UnitUpperTriangular

imported LinearAlgebra standard library into scope as LA. import LinearAlgebra: eigen as eig, cholesky as chol brings the eigen and cholesky meth- ods from LinearAlgebra into scope as eig and chol respectively individual identifiers are brought into scope. For example, using LinearAlgebra: eigen as eig or using LinearAlgebra: eigen as eig, cholesky as chol works, but using LinearAlgebra as LA is invalid syntax method for matrix-scalar operations is availableCHAPTER 77. LINEAR ALGEBRA 1231 Matrix type LAPACK eigen eigvals eigvecs svd svdvals Symmetric SY ARI Hermitian HE ARI UpperTriangular TR A A A UnitUpperTriangular

UniformScaling(2); julia> a = [1 2; 3 4] 2×2 Array{Int64,2}: 83.1. SPECIAL MATRICES 995 Matrix type LAPACK eigen eigvals eigvecs svd svdvals Symmetric SY ARI Hermitian HE ARI UpperTriangular TR A A A UnitUpperTriangular Pivoted QR factorization LQ QR factorization of transpose(A) Hessenberg Hessenberg decomposition Eigen Spectral decomposition GeneralizedEigen Generalized spectral decomposition SVD Singular value decomposition bunchkaufman, but saves space by overwriting the input A, instead of creating a copy. LinearAlgebra.Eigen – Type. 3J R Bunch and L Kaufman, Some stable methods for calculating inertia and solving symmetric